The requirement is simple. During Mughal rule, Muslims attempted to convert Sikhs, Hindus, Buddhists, Jains, etc. One of the ways this was done was forcing people to eat Halal meat, which was symbollic of the person accepting Islam. To prohibit this, the Gurus said that Sikhs should not eat Halal meat.

Therefore, the requirement has little to do with how the food is killed. It is more of a statement against how Islam was being practiced at the time.